Anomalous transport in the crowded world of biological cells

Abstract

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

review article, to appear in Rep. Prog. Phys

References in corpus (33)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
• Near-critical fluctuations and cytoskeleton-assisted phase separation lead to subdiffusion in cell membranes
• Relaxation Scenarios in a Mixture of Large and Small Spheres: Dependence on the Size Disparity
• Development of anomalous diffusion among crowding proteins
• Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Critical Dynamics in a Binary Fluid: Simulations and Finite-size Scaling
• Single-particle and collective slow dynamics of colloids in porous confinement
• Weakly non-ergodic Statistical Physics
• Generalized Elastic Model yields Fractional Langevin Equation
• Anisotropic memory effects in confined colloidal diffusion
• Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
• The Localization Transition of the Two-Dimensional Lorentz Model
• Diffusion-limited reactions in crowded environments
• Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
• Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
• Persistent correlation of constrained colloidal motion
• Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
• Anomalous transport resolved in space and time by fluorescence correlation spectroscopy
• Universal fluctuations in subdiffusive transport
• Correction-to-scaling exponent for two-dimensional percolation
• Persistent memory for a Brownian walker in a random array of obstacles
• Multi-point Distribution Function for the Continuous Time Random Walk
• Simulational study of anomalous tracer diffusion in hydrogels
• Dynamic arrest of colloids in porous environments: disentangling crowding and confinement
• Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach
• Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory
• Dynamic arrest in model porous media -- intermediate scattering functions
• Space-resolved dynamics of a tracer in a disordered solid
• Localization phenomena in models of ion-conducting glass formers
• Random walk approach to the d-dimensional disordered Lorentz gas

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• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• The role of fractional time-derivative operators on anomalous diffusion
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Diffusion-limited reactions in dynamic heterogeneous media
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• Non-universal tracer diffusion in crowded media of non-inert obstacles
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• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
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• Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
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• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Collective dynamics effect transient subdiffusion of inert tracers in gel networks
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Continuous-time random walks with reset events: Historical background and new perspectives
• Aging Scaled Brownian Motion
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Ageing underdamped scaled Brownian motion: ensemble and time averaged particle displacements, non-ergodicity, and the failure of the overdamping approximation
• Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond
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• On the stochastic thermodynamics of fractional Brownian motion
• Continuous time random walks and Lévy walks with stochastic resetting
• Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether
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• Stochastic Tools Hidden Behind the Empirical Dielectric Relaxation Laws
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• Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions
• Particle transport in hybrid PIC shock simulations: A comparison of diagnostics
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• Random motion of a circle microswimmer in a random environment
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• Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects
• Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
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• Diffusion of tagged particles in a crowded medium
• Ergodic property of random diffusivity system with trapping events
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• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Detection of Transition Times from Single-particle-tracking Trajectories
• Anomalous Fluctuations of Extremes in Many-Particle Diffusion
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• Dynamic heterogeneities and non-Gaussian behavior in two-dimensional randomly confined colloidal fluids
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• Tracer Diffusion on a Crowded Random Manhattan Lattice
• Extreme statistics of anomalous subdiffusion following a fractional Fokker-Planck equation: Subdiffusion is faster than normal diffusion
• Subdiffusive-Brownian crossover in membrane proteins: a Generalized Langevin Equation-based approach
• Persistence-Length Renormalization of Polymers in a Crowded Environment of Hard Disks
• Correlated Noise and Critical Dimensions
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• Fractional Brownian motion with fluctuating diffusivities
• Rectification and non-Gaussian diffusion in heterogeneous media
• Dynamically Crowded Solutions of Infinitely Thin Brownian Needles
• Anomalous transport of small polarons arises from transient lattice relaxation or immovable boundaries
• Multifractional Brownian motion with telegraphic, stochastically varying exponent
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• Generalized master equation for first-passage problems in partitioned spaces
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